{"department":[{"_id":"MaKw"}],"article_processing_charge":"Yes (via OA deal)","ec_funded":1,"abstract":[{"text":"In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs H in Kn, defined as the minimum number of colours needed to colour the edges of K so that every copy of a graph H E H intersects some colour class in an odd number of edges. In this paper, we focus on complete bipartite graphs. First, we completely resolve the problem when H is the family of all spanning complete bipartite graphs on n vertices. We then focus on its subfamilies, that is, {Kt,n-t : t E T} for a fixed set of integers T c [[n/2]]. We prove that the odd-Ramsey problem is equivalent to determining the maximum dimension of a linear binary code avoiding codewords of given weights, and leverage known results from coding theory to deduce asymptotically tight bounds in our setting. We conclude with bounds for the odd-Ramsey numbers of fixed (that is, non-spanning) complete bipartite subgraphs.","lang":"eng"}],"publication":"European Journal of Combinatorics","oa_version":"Published Version","external_id":{"arxiv":["2410.05887"]},"_id":"20482","year":"2025","publication_identifier":{"issn":["0195-6698"]},"language":[{"iso":"eng"}],"citation":{"ieee":"S. Boyadzhiyska, S. Das, T. Lesgourgues, and K. H. Petrova, “Odd-Ramsey numbers of complete bipartite graphs,” <i>European Journal of Combinatorics</i>, vol. 131. Elsevier, 2025.","apa":"Boyadzhiyska, S., Das, S., Lesgourgues, T., &#38; Petrova, K. H. (2025). Odd-Ramsey numbers of complete bipartite graphs. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">https://doi.org/10.1016/j.ejc.2025.104235</a>","ista":"Boyadzhiyska S, Das S, Lesgourgues T, Petrova KH. 2025. Odd-Ramsey numbers of complete bipartite graphs. European Journal of Combinatorics. 131, 104235.","mla":"Boyadzhiyska, Simona, et al. “Odd-Ramsey Numbers of Complete Bipartite Graphs.” <i>European Journal of Combinatorics</i>, vol. 131, 104235, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">10.1016/j.ejc.2025.104235</a>.","chicago":"Boyadzhiyska, Simona, Shagnik Das, Thomas Lesgourgues, and Kalina H Petrova. “Odd-Ramsey Numbers of Complete Bipartite Graphs.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">https://doi.org/10.1016/j.ejc.2025.104235</a>.","short":"S. Boyadzhiyska, S. Das, T. Lesgourgues, K.H. Petrova, European Journal of Combinatorics 131 (2025).","ama":"Boyadzhiyska S, Das S, Lesgourgues T, Petrova KH. Odd-Ramsey numbers of complete bipartite graphs. <i>European Journal of Combinatorics</i>. 2025;131. doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104235\">10.1016/j.ejc.2025.104235</a>"},"PlanS_conform":"1","intvolume":"       131","main_file_link":[{"url":"https://doi.org/10.1016/j.ejc.2025.104235","open_access":"1"}],"ddc":["500"],"month":"09","title":"Odd-Ramsey numbers of complete bipartite graphs","OA_type":"hybrid","has_accepted_license":"1","arxiv":1,"type":"journal_article","corr_author":"1","oa":1,"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"day":"13","OA_place":"publisher","volume":131,"author":[{"last_name":"Boyadzhiyska","first_name":"Simona","full_name":"Boyadzhiyska, Simona"},{"full_name":"Das, Shagnik","last_name":"Das","first_name":"Shagnik"},{"full_name":"Lesgourgues, Thomas","first_name":"Thomas","last_name":"Lesgourgues"},{"first_name":"Kalina H","last_name":"Petrova","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","full_name":"Petrova, Kalina H"}],"date_updated":"2025-10-23T09:26:53Z","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"article_number":"104235","scopus_import":"1","article_type":"original","acknowledgement":"The authors would like to thank Gilles Zémor for a helpful clarification on [3], Deepak Bal and Patrick Bennett for bringing [25] to their attention, and both referees for several helpful comments.\r\nS.B.: Most of this research was conducted while the author was at the School of Mathematics, University of Birmingham, Birmingham, United Kingdom. The research leading to these results was supported by EPSRC, United Kingdom, grant no. EP/V048287/1 and by ERC Advanced Grants “GeoScape”, no. 882971 and “ERMiD”, no. 101054936. There are no additional data beyond that contained within the main manuscript.\r\nS.D.: Research supported by Taiwan NSTC grants 111-2115-M-002-009-MY2 and 113-2628-M-002-008-MY4.\r\nK.P.: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. Parts of this research was conducted while K.P. was at the Department of Computer Science, ETH Zürich, Switzerland, supported by Swiss National Science Foundation, Switzerland , grant no. CRSII5 173721.","date_created":"2025-10-16T13:14:34Z","date_published":"2025-09-13T00:00:00Z","quality_controlled":"1","doi":"10.1016/j.ejc.2025.104235","publisher":"Elsevier","publication_status":"epub_ahead","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}